Numbers of individuals evaluated for rust resistance in a single population × environment (season) combination and across environments (seasons), variance component estimation, heritability, and genetic correlation between environments.

Pearson’s correlation (ρ) between observed and predicted stem rust values using four genomic selection models trained under three different conditions in five wheat populations evaluated in two seasons.

Model†

Population

BL

SVR-linear

SVR-RBF

RR

BL

SVR-linear

SVR-RBF

RR

Case A‡¶

TRN = TST = Off

TRN = TST = Main

PBW343 × Juchi

0.38

0.26

0.41

0.41

0.55

0.55

0.52

0.56

PBW343 × Kingbird

0.75**

0.66

0.64

0.68

0.69**

0.61

0.59

0.60

PBW343 × K-Nyangumi

0.59**

0.52

0.55

0.56

0.39

0.39

0.32

0.37

PBW343 × Muu

0.57*

0.50

0.53

0.56

0.62*

0.53

0.57

0.61

PBW343 × Pavon76

0.68**

0.55

0.58

0.60

0.60**

0.46

0.50

0.52

Case B§¶

TRN = Main + Off TST = Off

TRN = Main + Off TST = Main

PBW343 × Juchi

0.49 (28.9)

0.39 (50.0)

0.39 (−0.01)

0.53** (29.3)

0.58** (5.5)

0.45 (−18.2)

0.45 (−13.5)

0.47 (−16.1)

PBW343 × Kingbird

0.85** (13.3)

0.78 (18.2)

0.69 (7.8)

0.82 (20.6)

0.80 (15.9)

0.76 (24.6)

0.59 (0.0)

0.81* (35.0)

PBW343 × K-Nyangumi

0.74 (25.4)

0.66 (26.9)

0.78** (41.8)

0.65 (16.1)

0.70** (79.5)

0.67 (71.8)

0.62 (93.8)

0.62 (67.6)

PBW343 × Muu

0.72 (26.3)

0.72 (44.0)

0.55 (3.8)

0.75** (33.9)

0.78** (25.8)

0.75 (41.5)

0.60 (5.3)

0.72 (18.0)

PBW343 × Pavon76

0.78** (8.8)

0.66 (20.0)

0.71 (22.4)

0.72 (20.0)

0.70 (16.7)

0.67 (45.7)

0.64 (28.0)

0.70 (34.6)

Case C¶

TRN = Main TST = Off

TRN = Off TST = Main

PBW343 × Juchi

0.47

0.47

0.47

0.5

0.5

0.47

0.48

0.47

PBW343 × Kingbird

0.81

0.77

0.77

0.79

0.80

0.77

0.77

0.80

PBW343 × K-Nyangumi

0.61

0.64

0.62

0.62

0.62

0.67

0.67

0.61

PBW343 × Muu

0.77

0.77

0.77

0.80

0.80

0.77

0.80

0.77

PBW343 × Pavon76

0.70

0.68

0.68

0.68

0.70

0.69

0.63

0.68

*Best result for each environment × population combination is statistically significant at the 0.05 probability levels.

**Best result for each environment × population combination is statistically significant at the 0.01 probability levels.

‡The first two upper sections show the mean Pearson’s correlation (ρ) between observed and predicted stem rust values of 50 random partitions of the data for four models in five wheat populations evaluated in two seasons, off and main seasons. Models were trained and tested using three different combinations of training set (TRN) and testing set (TST). Case A: training and testing in the same environment. Case B: training in main plus off season and testing only in off season or only in main season. Case C: training in one season and predicting in the other.

§Numbers in parenthesis denote the percentage increase (or decrease) in the models’ prediction ability for Case B compared to their respective models in Case A.

Pairwise Pearson’s correlation (without reciprocals) between observed and predicted stem rust values of four different models. Algorithms were trained in one population (across both environments) and evaluated on the other population.

Testing or training†

PBW343 × Juchi

PBW343 × Kingbird

PBW343 × K-Nyangumi

PBW343 × Muu

PBW343 × Pavon76

Training or testing‡

PBW343 × Juchi

–

0.48

0.14

0.28

0.31

Bayes LASSO

PBW343 × Kingbird

0.53

–

0.29

0.25

0.54

PBW343 × K-Nyangumi

0.14

0.30

–

0.28

0.28

PBW343 × Muu

0.18

0.30

0.33

–

0.29

PBW343 × Pavon76

0.37

0.51

0.22

0.33

–

Ridge regression

Testing or training§

PBW343 × Juchi

PBW343 × Kingbird

PBW343 × K-Nyangumi

PBW343 × Muu

PBW343 × Pavon76

Training or testing

PBW343 × Juchi

–

0.28

0.32

0.48

0.32

SVR-linear

PBW343 × Kingbird

0.28

–

0.45

0.53

0.59

PBW343 × K-Nyangumi

0.35

0.31

–

0.25

0.39

PBW343 × Muu

0.14

0.58

0.26

–

0.55

PBW343 × Pavon76

0.35

0.64

0.41

0.67

–

SVR-RBF

†The upper-right triangle of the first section of the table has the results of Bayes least absolute shrinkage and selection operator (LASSO), with the rows indicating the training population and the columns the testing population.

‡The lower-left triangle gives the results of ridge regression, with the columns indicating the training population and the rows the test population.

§The second section of the table shows similar results in the upper-right and lower-left triangles but considers support vector regression with linear kernel (SVR-linear) and support vector regression with radial basis function kernel (SVR-RBF).

Pearson’s correlation (ρ) between observed and predicted yellow rust values for four models trained under three different conditions in five wheat populations evaluated in two sites Njoro (Kenya) and Toluca (Mexico).

Model†

Population

BL

SVR-linear

SVR-RBF

RR

BL

SVR-linear

SVR-RBF

RR

Case A‡¶

TRN = TST = Njoro

TRN = TST = Toluca

PBW343 × Juchi

0.33

0.42*

0.41

0.33

0.37

0.37

0.34

0.37

PBW343 × Kingbird

0.23**

0.16

0.14

0.20

0.49

0.42

0.48

0.49

PBW343 × K Nyangumi

–

–

–

–

0.30**

0.24

0.23

0.15

PBW343 × Muu

0.17

0.19

0.20*

0.12

0.49

0.45

0.46

0.49

PBW343 × Pavon76

0.26

0.20

0.33**

0.25

0.63**

0.54

0.58

0.59

Case B§¶

TRN = Njoro + Toluca TST = Njoro

TRN = Njoro + Toluca TST = Toluca

PBW343 × Juchi

0.56 (69.7)

0.53 (26.2)

0.52 (26.9)

0.56 (69.7)

0.63 (70.3)

0.60 (62.2)

0.60 (44.1)

0.52 (40.5)

PBW343 × Kingbird

0.36** (60.9)

0.30 (100)

0.33 (135.7)

0.32 (60.0)

0.50* (2.0)

0.31 (−26.1)

0.47 (−14.6)

0.45 (−8.2)

PBW343 × Muu

0.19 (11.8)

0.15 (−21.1)

0.20 (0.0)

0.14 (16.7)

0.29 (−40.8)

0.34 (−24.0)

0.06 (−87.0)

0.26 (−47.0)

PBW343 × Pavon76

0.46 (76.9)

0.46 (130.0)

0.46 (39.4)

0.45 (80.0)

0.62** (−1.6)

0.47 (−13.0)

0.56 (−3.45)

0.60 (1.69)

Case C¶

TRN = Toluca TST = Njoro

TRN = Njoro TST = Toluca

PBW343 × Juchi

0.52

0.52

0.52

0.54

0.52

0.52

0.52

0.56

PBW343 × Kingbird

−0.09

0.30

0.31

−0.10

−0.16

0.34

0.42

0.10

PBW343 × Muu

0.18

0.13

0.13

0.18

0.17

0.15

0.15

0.17

PBW343 × Pavon76

0.48

0.47

0.47

0.48

0.47

0.44

0.41

0.45

*Best result for each environment × population combination is statistically significant at the 0.05probability levels.

**Best result for each environment × population combination is statistically significant at the 0.01 probability levels.

‡The two upper sections show the mean Pearson’s correlation (ρ) between observed and predicted yellow rust values of 50 random partitions of the data for four models in five wheat populations evaluated in two sites Njoro (Kenya) and Toluca (Mexico). Models were trained and tested using three different combinations of training set (TRN) and testing set (TST). Case A: training and testing in the same environment. Case B: training in Njoro plus Tolca and testing only in Njoro or only in Toluca. Case C: training in one environment and predicting in the other.

§Numbers in parentheses denote the percentage increase (or decrease) in the models’ predictive ability for Case B compared to their respective models in Case A.

Pairwise Pearson’s correlation (without reciprocals) between observed and predicted yellow rust values for four different models. The algorithms were trained in one population (across both environments) and evaluated in the other population.

Testing or training

PBW343 × Juchi

PBW343 × Kingbird

PBW343 × Muu

PBW343 × Pavon76

Training or testing

PBW343 × Juchi

–

0.12

0.06

0.09

Bayesian LASSO†

PBW343 × Kingbird

0.06

–

0.16

0.14

PBW343 × Muu

0.05

0.16

–

0.07

PBW343 × Pavon76

0.10

0.14

0.09

–

Ridge regression‡

Testing or training

PBW343 × Juchi

PBW343 × Kingbird

PBW343 × Muu

PBW343 × Pavon76

Training or testing

PBW343 × Juchi

–

0.09

0.05

0.07

SVR-linear§

PBW343 × Kingbird

0.09

–

0.04

0.21

PBW343 × Muu

0.09

0.11

–

0.09

PBW343 × Pavon76

0.12

0.18

0.12

–

SVR-RBF

†The upper-left triangle in the first section of the table shows the results of Bayesian least absolute shrinkage and selection operator (LASSO), with the rows indicating the training population and the columns the testing population.

‡The lower-left triangle shows the results of ridge regression, with the columns indicating the training population and the rows the test population.

§The second section of the table shows similar results in the upper and lower triangles but considering support vector regression with linear kernel (SVR-linear) and support vector regression with radial basis function (SVR-RBF) kernel.